Showing papers on "MDS matrix published in 2011"

Direct Exponent and Scalar Multiplication Classes of an MDS Matrix.

Abstract: Ghulam Murtaza, Nassar Ikram 1,2 National University of Sciences and Technology, Pakistan azarmurtaza@hotmail.com dr_nassar_ikram@yahoo.com Abstract. An MDS matrix is an important building block adopted by different algorithms that provides diffusion and therefore, has been an area of active research. In this paper, we present an idea of direct exponent and direct square of a matrix. We prove that direct square of an MDS matrix results in an MDS matrix whereas direct exponent may not be an MDS matrix. We also delineate direct exponent class and scalar multiplication class of an MDS matrix and determine the number of elements in these classes. In the end, we discuss the standing of design properties of a cryptographic primitive by replacing MDS matrix by dynamic one.

A method for linear transformation in substitution-permutation network symmetric-key block cipher

Abstract: One embodiment of the present invention is a method of linear transformation in Substitution-Permutation Network symmetric-key block cipher producing n x n key-dependent MDS matrices from given n x n MDS matrix by scalar multiplication and permutations of elements of given matrix where multiplicative scalar and permutations are derived from binary inputs of length l . The method comprising deriving multiplicative scalar from binary input; multiplying given matrix with multiplicative scalar, producing first intermediate matrix; deriving first permutation of n objects from binary input; permuting rows of first intermediate matrix according to first permutation, producing second intermediate matrix; deriving second permutation of n objects from binary input; and permuting columns of second intermediate matrix according to second permutation to produce final MDS matrix. Another embodiment of the present invention is a method of linear transformation in Substitution-Permutation Network symmetric-key block cipher producing n x n key-dependent MDS matrices from given n x n MDS matrix by scalar multiplication and permutations of elements of given matrix where multiplicative scalar and permutations are derived from binary inputs of length l . The method comprising deriving multiplicative scalar from the key (202); multiplying given matrix with multiplicative scalar to produce first intermediate matrix (204); deriving first permutation of n objects from the key (206); permuting rows of first intermediate matrix according to first permutation to produce second intermediate matrix (208); deriving second permutation of n objects from the key (304); and permuting columns of second intermediate matrix according to second permutation (212) to produce final MDS matrix (214).

Perfect involutory diffusion layers based on invertibility of some linear functions

Abstract: One of the most important structures used in modern block ciphers is the substitution-permutation network (SPN) structure. Many block ciphers with this structure widely use Maximun Distance Separable (MDS) matrices over finite fields as their diffusion layers, for example, advanced encryption standard (AES) uses a 4-4 MDS matrix as the main part of its diffusion layer and the block cipher Khazad has an involutory 8-8 matrix. In this study, first a construction is proposed for a 4-4 linear diffusion layer that can intermix four words of arbitrary size with branch number 5. Then extend this idea for 8-8 diffusion layer using low-cost linear functions. In this construction, first, certain binary linear combinations of inputs are fed into two or three different invertible linear functions and then combined using XOR operation. In order to show the efficiency of the proposed diffusion layer, the authors exploit it in a nested SPN structure and compare its efficiency with some well-known diffusion layers such as the diffusion layer of Hierocrypt.

Encryption device encryption method and record medium

Abstract: The invention realizes a high-security cryptographic processing apparatus that increases difficulty in analyzing its key and a method therefor. In Feistel-type common-key-block cryptographic processing that repeatedly executes an SPN-type F-function having the nonlinear conversion section and the linear conversion section over a plurality of rounds, Linear conversion processing of an F-function corresponding to each of the plurality of rounds is carried out by linear conversion processing that applies square MDS (Maximum Distance Separable) matrices. The invention uses a setting that arbitrary m column vectors included in inverse matrices of square MDS matrices being set up at least in consecutive even-numbered rounds and in consecutive odd-numbered rounds, respectively, constitute a square MDS matrix. This structure realizes cryptographic processing whereby resistance to linear cryptanalysis attacks in the common-key-block cipher is improved.

Improving the Diffusion power of AES Rijndael with key multiplication

Abstract: Block ciphers are very important in communication systems as they provide confidentiality through encryption. The popular block cipher is an Advanced Encryption Standard (AES). Each cipher uses several rounds of fixed operations to achieve desired security level. The number of rounds in a block cipher is decided based upon the resistivity levels against the known attacks. The very first level of attack on an encryption algorithm is to search for repetitive cipher values and relate them to plaintext. The diffusion enables to spread out the repetitive plain text patterns in the cipher values. The diffusion is achieved using linear operations such as key addition, rotate byte, MDS matrix multiplication, etc. In this paper we propose a method of enhancing the diffusion power by key multiplication rather than conventional key addition used in the Advanced encryption standard algorithm. The paper discusses the problems associated with the key multiplication and provides the possible solutions. The measured results indicate more diffusion when compared with the existing method. Key multiplication, as a diffusion element, is a better solution in the design of encryption algorithms.